A large part of Seven of Nine's story arc is her attempt to become human again.
Why then, do they continue to refer to her as Seven of Nine? At some point they learn her real name, Annika Hansen.
I can understand when she is confronting the Borg Queen, the Queen may refuse to call her by her real name, but how do you explain the rest of the Voyager crew?
This is explained soon after she joins the crew.
In Season 4, Episode 3 (Day of Honor) Captain Janeway suggests using her human name Annika.
However, the only identity she remembers ever using is Seven of Nine, so she has no desire to use her original name. Janeway suggests simply "Seven", which she agrees too.
Janeway: Your designation, Seven of Nine, it's a little cumbersome. Wouldn't you prefer to be called by your given name, Annika?
Seven: I have been Seven of Nine for as long as I can remember.
Janeway: All right. But maybe we could streamline it a little. How would you feel about Seven?
Seven: Imprecise, but acceptable.
You can read the full transcript here.
That said, she does continue to use use "Seven of Nine" (Tertiary Adjunct of Unimatrix 01) when referring to herself formally, often when dealing with the Borg, or referring to herself as one. Everyone else just calls her Seven for simplicity.
Because that is the name she choose for herself and that is who she is.
'Seven of Nine' is more 'her' than 'Annika Hansen' will ever be. The young girl was assimilated and, for all intents and purposes, died, when she became part of the Collective and was turned into Seven of Nine.
In the episode Survival Instinct (S06E02), it is clearly shown that Seven is the only identity that she has. The Sphere she was on crashed on a remote planet, and she ended up with three other Borgs on the planet. Those Borgs start to regain memories of their previous lives because they were assimilated as adults. Seven was assimilated as a child and has little to return to.
The Raven wasn't discovered until several months after they 'freed' Seven of Nine, and it is obvious in later episodes, as she explores the archives retrieved from the ship, that she feels little connection to her previous identity or her family and is even a bit resentful that they took her on their scientific journey chasing what was essentially a rumor when they set out. A rumor that turned out to be very dangerous.
From S05E15/16 'Dark Frontier':
JANEWAY: I'd like to narrow that list of variables. I was hoping your parents might provide us with a few insights. I've been looking over the records we found on the U.S.S. Raven. Your parents kept extensive field notes, detailed journals. There are over nine thousand log entries alone.
SEVEN: The information is irrelevant.
JANEWAY: On the contrary, Seven. They spent their careers studying the Borg. They tracked a cube at close range for what, two years?
SEVEN: Three.
JANEWAY: Well, I'd say that made them experts. I want you to study their research. Look for any data that might give us a tactical edge.
SEVEN: My parents were assimilated. Obviously their tactics were flawed.
JANEWAY: Look, these records have been collecting dust in our database for over a year. You say they're irrelevant, and I say you've been avoiding them. You're the best person for the job, but I'll assign it to Chakotay if I
SEVEN: No. The information belongs to me. I will read it.
[Cargo Bay two]
(Neelix brings in a case of PADDs.)
SEVEN: You're late.
NEELIX: Sorry. It took longer than I expected to download these records. This is only the first batch. Your parents sure had a lot to say. I organised the information by category. Field notes, personal logs, biokinetic analyses. I don't mean to pry, but is it true your parents were studying the Borg?
SEVEN: Yes. The Hansens were exobiologists.
NEELIX: Fascinating. They must have been very courageous.
SEVEN: They were misguided.
[...]
SEVEN: My parents underestimated the Collective. They were destroyed. Because of their arrogance, I was raised by Borg.
As for the Voyager crew, being from the enlightened society that is the United Federation of Planets, they respected her choice of name. While it could be argued that they kept on calling her Seven because that was the only name they had for her at the beginning, there is little doubt that they would have switched to Annika, or whatever other name she might have chosen, if she decided to shed the Borg designation in favor of something more in tune with her human side.
In addition to the other excellent answers here, I believe Seven has a fundamental internal conflict. On the one hand she is angry with her parents for getting her assimilated, and hence doesn't want anything to do with them. But on the other hand the only other identity she has is as a Borg. Her anger with her parents implies that she regards being assimilated as a Bad Thing, but that same anger prevents her from reclaiming her identity as Annika.
By being "Seven of Nine" she can treat her feelings of anger as "irrelevant", and hence present a cold, hard unemotional persona which protects the vulnerable child Annika who is still hiding inside.
She's a conflicted person who originally thinks she's more Borg than human. This is repeatedly tested, time and again through out the show. Even to the point where she runs Janeway’s holo programs to understand her own nature.
Though she accepts the idea of Annika Hansen eventually, she still feels compelled to being more Borg but not less human overtime. Lest we forget she is the person who rescued abandoned Borg children, that would go on to serve as examples of what it is to be human. Nearing the show’s end we see a different kind of Seven; one who is less Borg, and starting to accept her human qualities. She even went the route of asking the doctor for advice, and ran simulations with crew interactions.
It seems like her identity is a form of conflict of natures, or perhaps the best way for the show’s creators to emphasize a moral self guided lesson: “Who am I?”
